We deal with a class of 2-D stationary nonlinear Schrödinger equations (NLS) involving potentials V and weights Q decaying to zero at infinity as (1 + | x| α) - 1, α∈ (0 , 2) , and (1 + | x| β) - 1, β∈ (2 , + ∞) , respectively, and nonlinearities with exponential growth of the form exp γ0s2 for some γ0> 0. Working in weighted Sobolev spaces, we prove the existence of a bound state solution, i.e. a solution belonging to H1(R2). Our approach is based on a weighted Trudinger–Moser-type inequality and the classical mountain pass theorem.

Stationary nonlinear Schr"odinger equations in $BbbR^2$ with potentials vanishing at infinity / do O, Joao Marcos; Sani, Federica; Zhang, Jianjun. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 196:1(2017), pp. 363-393. [10.1007/s10231-016-0576-5]

Stationary nonlinear Schr"odinger equations in $BbbR^2$ with potentials vanishing at infinity

Sani, Federica;
2017

Abstract

We deal with a class of 2-D stationary nonlinear Schrödinger equations (NLS) involving potentials V and weights Q decaying to zero at infinity as (1 + | x| α) - 1, α∈ (0 , 2) , and (1 + | x| β) - 1, β∈ (2 , + ∞) , respectively, and nonlinearities with exponential growth of the form exp γ0s2 for some γ0> 0. Working in weighted Sobolev spaces, we prove the existence of a bound state solution, i.e. a solution belonging to H1(R2). Our approach is based on a weighted Trudinger–Moser-type inequality and the classical mountain pass theorem.
2017
196
1
363
393
Stationary nonlinear Schr"odinger equations in $BbbR^2$ with potentials vanishing at infinity / do O, Joao Marcos; Sani, Federica; Zhang, Jianjun. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 196:1(2017), pp. 363-393. [10.1007/s10231-016-0576-5]
do O, Joao Marcos; Sani, Federica; Zhang, Jianjun
File in questo prodotto:
File Dimensione Formato  
VOR_Stationary nonlinear Schrödinger.pdf

Open access

Tipologia: Versione pubblicata dall'editore
Dimensione 640.69 kB
Formato Adobe PDF
640.69 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1187056
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 30
  • ???jsp.display-item.citation.isi??? 28
social impact